Yuan Yuan
Google
Certainly the meatiest sight that we visited in Reykjavik, covers the history of Iceland from Viking settlement (there were rumors but no evidence of Irish monks beforehand) until present day. The exhibits pre-Christianity were quite interesting, post-Christianity the content felt much less uniquely Icelandic, and there was quite a bit of it. The museum felt like it glided shallowly over some of the most interesting and tense moments of Icelandic history, for example the conversion to Christianity, Reformation, WWII occupation, and full independence from Denmark. That being said it was probably the most significant sight in Reykjavik in which we partook.